Image Processing Reference
In-Depth Information
It is worth noting that in image analysis applicatons, all directions may not have
the same physical meaning. This implies that distances in the
N
-dimensional space
on which
f
, and thereby
S
is defined may lack physical relevance, although direc-
tions may still be meaningful. For example, in a TV sequence, the first two dimen-
sions are length, whereas the third dimension is time, e.g., see Figs. 12.2 and 12.1.
Depending on what unit has been chosen for the time (seconds or hours) and the
length (meter or km) and whether or not the points are in the same image frame, the
interpretation of the Euclidean length between two points in the 3D spatio-temporal
sequence will be different. However, the direction of lines and planes will represent
the velocity, a physically meaningful quantity. We will discuss the spatio-temporal
direction below.
12.4 Basic Concepts of Image Motion
Visual motion analysis is a vital processing element of the mammalian visual sys-
tems, which include human vision. Even still image processing, which would nor-
mally be handled by still image analysis tools in computer vision, are handled via
motion analysis pathways of the brain. For example, even when analyzing a painting
on the wall, the human eyes perform saccades, whereby the motif is brought to an
artificial motion on the retina to the effect that the relevant visual field is analyzed
by the cells of the brain that are motion-direction, and/or spatial-direction sensitive.
While the current understanding of mammalian vision still leaves room for discus-
sion on the reasons why biological vision has gone to 3D signal analysis to solve
2D problems, it is beyond doubt that motion is a very valuable and powerful feature.
By contrast, it is fair to say that much of the development efforts in computer vision
have been steered towards still image analysis tools essentially because of the limi-
tations in computational resources, even if the power of motion in image analysis is
not a disputed issue. However, because of the rapid developments in computer and
communication technologies, this argument is swiftly being suppressed as a raison
d'etre.
The motion of a body can be observed by an eye or by artificial imaging equip-
ment. In this section we will discuss the translational motion of a local patch, as this
is a good starting point to approximate even more complex types of motions, e.g.,
those that can bring an image into rotation. We discuss the motion of a surface patch
of a 3D object moving relative to a camera in a small time interval. The velocity
of the motion is a 3D vector. When the moving patch is observed by a camera (on
a 2D plane), the light reflections from the surface are projected to the image plane.
Also, the 3D velocity vector is projected to the image plane, now becoming a 2D
vector field. The vector field representing the translations of the moving object sur-
face patches is known as the
motion field
. Whether or not the motion field is actually
identifiable by a vision system from the observed projections of the object surface
depends on many factors, such as the surface color, its texture, the optical properties
of the material when interacting with light, and the illumination. The observable ver-
sion of the motion field is known as
optical flow
. In many circumstances the optical
